I work at a hospital that is doing research on the vaccines, and they recently did a video explaining how they work, what the potential side-effects are, and some general numbers.
1) The rate at which individuals experience initial side-effects is something around 10-15%, but this is often just a minor fever and passes within a few days. This is why they have you wait for around 15 minutes prior to leaving after getting the vaccine.
2)The rates of serious reaction (not death) to the vaccine is 7 in 1,000,000, so if you aren't worried about Covid because the survival rate is 99.7%, you shouldn't be worried about this either.
Also, anyone worried about it should just research how mRNA works. The tech going into these vaccines is actually remarkable, and will ultimately change the way we do future vaccines. This vaccine is actually arguably safer than a flu shot, as the risk for an allergic reaction is basically none.